Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
594 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#634 | C2 | semidirect |
| 3. C2×C3×#208 | C2 | semidirect |
| 4. C2×#3719 | C2 | semidirect |
| 5. #63831 | C2 | direct (N × H) |
| 6. C2×#3716 | C2 | semidirect |
| 14. C2×#634 | C22 | semidirect |
| 21. C3×#208 | C22 | semidirect |
| 23. #3719 | C22 | semidirect |
| 24. #3716 | C22 | semidirect |
| 34. C2×#208 | D3 | semidirect |
| 92. #208 | C2×D3 | semidirect |
| 161. C2×C32 | #137 | semidirect |
| 207. C32 | C2×#137 | semidirect |
| 233. C2×C3 | #909 | semidirect |
| 234. C2×C3 | #951 | semidirect |
| 249. C3 | C2×#909 | semidirect |
| 250. C3 | C2×#951 | semidirect |
| 253. C2 | #63831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634 | 2 |
| C2×C3×#235 | 2 |
| C2×C3×#208 | 2 |
| C2×#3719 | 2 |
| #63831 | 2 |
| C2×#3716 | 2 |
| C2×#951 | 3 |
| C2×#909 | 3 |